**Boyce E. Griffith**

Assistant Professor of Mathematics

Adjunct Assistant Professor of Biomedical Engineering

Member, McAllister Heart Institute

University of North Carolina at Chapel Hill

email: boyceg@email.unc.edu

phone: 919.962.1294 (office), 919.962.2568 (fax)

web: http://www.cims.nyu.edu/~griffith

Software

**IBAMR:** IBAMR is a
distributed-memory parallel implementation of the immersed
boundary (IB) method with support for Cartesian grid adaptive
mesh refinement (AMR). Support for distributed-memory
parallelism is via MPI, the Message Passing Interface. Support
for spatial adaptivity is via SAMRAI, the
Structured Adaptive Mesh Refinement Application Infrastructure,
which is developed at the Center for Applied
Scientific Computing at Lawrence Livermore National
Laboratory.

This implementation of the IB method also makes extensive use of functionality provided by several high-quality third-party software libraries, including:

- PETSc, the Portable, Extensible Toolkit for Scientific Computation,
*hypre*, a library of high performance preconditioners that features parallel multigrid methods for both structured and unstructured grid problems,- HDF5, a general purpose library and file format for storing scientific data,
- Blitz++, a high-performance C++ array class library, and
- Silo, a general purpose I/O library and file format for storing scientific data for visualization and post-processing.

IBAMR outputs visualization files that can be
read by the VisIt
Visualization Tool. Work is also underway to implement
support for finite element mechanics models in IBAMR via the
`libMesh`

finite
element library.

IBAMR source code is hosted by GitHub at https://github.com/IBAMR/IBAMR.

Multi-beat simulations of the fluid dynamics of the aortic heart valve with physiological driving and loading conditions using the immersed boundary method.

**A model aortic valve is mounted in a
semi-rigid aortic root model with anatomically realistic aortic
sinuses.** This "valve tester" is immersed in a fluid box.
Pressure boundary conditions are imposed at the inlet (bottom)
of the vessel using a prescribed left ventricular pressure
waveform, and at the outlet (top) of the vessel using a
Windkessel model. (See schematic diagram below.)

**Schematic diagram showing how boundary
conditions are imposed on the model vessel.** At the upstream
boundary, a time-dependent left-ventricular pressure waveform
is prescribed. At the downstream boundary, the
three-dimensional fluid-structure interaction model is coupled
to a three-element Windkessel model fit to human data. Notice
that the flow rate is *not* prescribed in this model, but
rather emerges during the computation.

**The opening and closing dynamics of the model
aortic valve.** The lower inset shows the prescribed driving
pressure (blue curve) and computed loading pressure (green
curve). The upper inset shows the computed flow rate through
the model valve (blue curve). Net flow through the model valve
is approximately 65 ml per cardiac cycle, which is within the
physiological range. Notice that the flow rate is *not*
specified in the model; rather, it emerges during the course of
the fluid-structure interaction simulation. (Click on the above
images to view linked QuickTime movies.)

**The opening and closing dynamics of the model
aortic valve along with the axial (streamwise) fluid
velocity.** The fluid velocity is shown on a plane that
bisects the model vessel and one of the model valve leaflets.
Forward flow is indicated in red, reverse flow is indicated in
blue. Notice that, except for the first beat, the model valve
permits essentially no regurgitation during closure. (Click on
the above image to view linked QuickTime movie.)

For further details, see: B.E. Griffith. Immersed
boundary model of aortic heart valve dynamics with
physiological driving and loading conditions. *Int J Numer
Meth Biomed Eng*, 28:317-345, 2012. (DOI, PDF)

Simulations of a prosthetic mitral heart valve using the immersed boundary method.

A chorded prosthetic mitral valve (left panel) and the corresponding immersed boundary model (right panel).

**The model mitral valve is mounted in a rigid
tube that is immersed in a fluid box.** Time-dependent
velocity boundary conditions are prescribed at the upstream
boundary (located at the left of the figure) and zero-pressure
boundary conditions are prescribed at the downstream boundary
(located at the right of the figure).

**The opening and closing dynamics of the model
prosthetic mitral valve viewed from the side (left panel) and
top (right panel).** (Click on the above images to view
linked QuickTime movies.)

Streamlines during the opening phase of the model mitral valve.

For further details, see: B.E. Griffith, X.Y.
Luo, D.M. McQueen, and C.S. Peskin. Simulating the fluid
dynamics of natural and prosthetic heart valves using the
immersed boundary method. *Int J Appl Mech*, 1:137-177,
2009. (DOI, PDF)

**Simulations of the electrical function of the
heart by an immersed boundary approach to the bidomain
equations.**

Click on the above images to view the corresponding animated GIFs.

Simulations of cardiac fluid mechanics by an adaptive version of the immersed boundary method.

Click on the above images to view the corresponding animated GIFs. Additional animations are available here, and an overview of the three-dimensional fiber structure of the heart and great vessels used in this work is available here.

**Curriculum Vitae** (PDF)

**Research Interests**

Mathematical and computational methods in medicine and biology;
computer simulation in physiology, especially cardiovascular
mechanics and fluid-structure interaction, cardiac
electrophysiology, and cardiac electro-mechanical coupling;
adaptive numerical methods; high-performance computing

All peer-reviewed publications (in reverse chronological order by publication date)

- M. Cai, A. Nonaka, J.B. Bell, B.E. Griffith,
and A. Donev. Efficient variable-coefficient finite-volume
Stokes solvers.
*Comm Comput Phys*. To appear. - H. Gao, D. Carrick, C. Berry, B.E. Griffith,
and X.Y. Luo. Dynamic finite-strain modelling of the human
left ventricle in health and disease using an immersed
boundary-finite element method.
*IMA J Appl Math*. To appear. - H. Gao, H.M. Wang C. Berry, X.Y. Luo, and B.E.
Griffith. Quasi-static image-based immersed boundary-finite
element model of left ventricle under diastolic loading.
*Int J Numer Meth Biomed Eng*. To appear. - T.G. Fai, B.E. Griffith, Y. Mori, and C.S.
Peskin. Immersed boundary method for variable viscosity and
variable density problems using fast constant-coefficient
linear solvers. II: Theory.
*SIAM J Sci Comput*. To appear. - D.M. McQueen, T. O'Donnell, B.E. Griffith, and
C.S. Peskin. Constructing a Patient-Specific Model Heart from
CT Data. In N. Paragios, N. Ayache, and J. Duncan, editors,
*Handbook of Biomedical Imaging*. Springer-Verlag, New York, NY, USA. To appear. - T. Skorczewski, B.E. Griffith, and A.L.
Fogelson. Multi-bond models for platelet adhesion and
cohesion. In S.D. Olson and A.T. Layton, editors,
*Biological Fluid Dynamics: Modeling, Computation, and Applications*, Contemporary Mathematics, Providence, RI, USA. American Mathematical Society. To appear. - S. Delong, F. Balboa Usabiaga, R.
Delgado-Buscalioni, B.E. Griffith, and A. Donev. Brownian
dynamics without Green's functions.
*J Chem Phys*, 140(13):134110 (23 pages), 2014. (DOI) - F. Balboa Usabiaga, R. Delgado-Buscalioni,
B.E. Griffith, and A. Donev. Inertial Coupling Method for
particles in an incompressible fluctuating fluid.
*Comput Meth Appl Mech Eng*, 269:139-172, 2014. (PDF, DOI) - H.M. Wang, X.Y. Luo, H. Gao, R.W. Ogden, B.E.
Griffith, C. Berry, and T.J. Wang. A modified Holzapfel-Ogden
law for a residually stressed finite strain model of the
human left ventricle in diastole.
*Biomech Model Mechanobiol*, 3(1):99-113, 2014. (DOI) - A.P.S. Bhalla, R. Bale, B.E. Griffith, and
N.A. Patankar. Fully resolved immersed electrohydrodynamics
for particle motion, electrolocation, and self-propulsion.
*J Comput Phys*, 256:88-108, 2014. (PDF, DOI) - V. Flamini, A. DeAnda, and B.E. Griffith.
Simulating the effects of intersubject variability in aortic
root compliance by the immersed boundary method. In P.
Nithiarasu, R. Löhner, and K.M. Liew, editors,
*Proceedings of the Third International Conference on Computational & Mathematical Biomedical Engineering*, 2013. - X.S. Ma, H. Gao, N. Qi, C. Berry, B.E.
Griffith, and X.Y. Luo. Image-based immersed boundary/finite
element model of the human mitral valve. In P. Nithiarasu, R.
Löhner, and K.M. Liew, editors,
*Proceedings of the Third International Conference on Computational & Mathematical Biomedical Engineering*, 2013. - A.P.S. Bhalla, B.E. Griffith, N.A. Patankar,
and A. Donev. A minimally-resolved immersed boundary model
for reaction-diffusion problems.
*J Chem Phys*, 139(21):214112 (15 pages), 2013. (DOI) - B.E. Griffith, V. Flamini, A. DeAnda, and L.
Scotten. Simulating the dynamics of an aortic valve
prosthesis in a pulse duplicator: Numerical methods and
initial experience.
*J Med Dev*, 7(4):040912 (2 pages), 2013. (DOI) - B.E. Griffith and C.S. Peskin.
Electrophysiology.
*Comm Pure Appl Math*, 66(12):1837-1913, 2013. (DOI) - T.G. Fai, B.E. Griffith, Y. Mori, and C.S.
Peskin. Immersed boundary method for variable viscosity and
variable density problems using fast constant-coefficient
linear solvers. I: Numerical method and results.
*SIAM J Sci Comput*, 35(5):B1131-B1161, 2013. (DOI) - A.P.S. Bhalla, R. Bale, B.E. Griffith, and
N.A. Patankar. A unified mathematical framework and an
adaptive numerical method for fluid-structure interaction
with rigid, deforming, and elastic bodies.
*J Comput Phys*, 250:446-476, 2013. (DOI) - S.L. Maddalo, A. Ward, V. Flamini, B.
Griffith, P. Ursomanno, and A. DeAnda. Antihypertensive
strategies in the management of aortic disease.
*J Am Coll Surg*, 217(3):S39, 2013. (DOI) - H. Gao, B.E. Griffith, D. Carrick, C. McComb,
C. Berry, and X.Y. Luo. Initial experience with a dynamic
imaging-derived immersed boundary model of human left
ventricle. In S. Ourselin, D. Rueckert, and N. Smith,
editors,
*Functional Imaging and Modeling of the Heart: 7th International Conference, FIMH 2013, London, UK, June 20-22, 2013*, volume 7945 of*Lecture Notes in Computer Science*, pages 11-18, 2013. (DOI) - A.P.S. Bhalla, B.E. Griffith, and N.A.
Patankar. A forced damped oscillation framework for
undulatory swimming provides new insights into how propulsion
arises in active and passive swimming.
*PLOS Comput Biol*, 9(6):e100309 (16 pages), 2013. (DOI) - S. Delong, B.E. Griffith, E. Vanden-Eijnden,
and A. Donev. Temporal integrators for fluctuating
hydrodynamics.
*Phys Rev E*, 87(3):033302 (22 pages), 2013. (DOI, PDF) - X.S. Ma, H. Gao, B.E. Griffith, C. Berry, and
X.Y. Luo. Image-based fluid-structure interaction model of
the human mitral valve.
*Comput Fluid*, 71:417-425, 2013. (DOI, PDF) - H.M. Wang, H. Gao, X.Y. Luo, C. Berry, B.E.
Griffith, R.W. Ogden, and T.J. Wang. Structure-based finite
strain modelling of the human left ventricle in diastole.
*Int J Numer Meth Biomed Eng*, 29(1):83-103, 2013. (DOI, PDF) - F. Balboa Usabiaga, J.B. Bell, R.
Delgado-Buscalioni, A. Donev, T.G. Fai, B.E. Griffith, and
C.S. Peskin. Staggered schemes for fluctuating hydrodynamics.
*Multiscale Model Sim*, 10(4):1369-1408, 2012. (DOI, PDF) - B.E. Griffith and S. Lim. Simulating an
elastic ring with bend and twist by an adaptive generalized
immersed boundary method.
*Commun Comput Phys*, 12(2):433-461, 2012. (DOI, PDF) - B.E. Griffith. On the volume conservation of
the immersed boundary method.
*Commun Comput Phys*, 12(2):401-432, 2012. (DOI, PDF) - X.Y. Luo, B.E. Griffith, X.S. Ma, M. Yin, T.J.
Wang, C.L. Liang, P.N. Watton, and G.M. Bernacca. Effect of
bending rigidity in a dynamic model of a polyurethane
prosthetic mitral valve.
*Biomechan Model Mechanobiol*, 11(6):815-827, 2012. (DOI, PDF) - B.E. Griffith. Immersed boundary model of
aortic heart valve dynamics with physiological driving and
loading conditions.
*Int J Numer Meth Biomed Eng*, 28(3):317-345, 2012. (DOI, PDF; the published version of this paper includes significant typographical errors that were introduced by the publisher following the proofing process; these errors do not appear in the linked PDF document)

*Erratum:*B.E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions.*Int J Numer Meth Biomed Eng*, 29(5):698-700, 2013. (DOI) - P.E. Hand and B.E. Griffith. Empirical study
of an adaptive multiscale model for simulating cardiac
conduction.
*Bull Math Biol*, 73(12):3071-3089, 2011. (DOI, PDF) - P.E. Hand and B.E. Griffith. Adaptive
multiscale model for simulating cardiac conduction.
*Proc Natl Acad Sci U S A*, 107(33):14603-14608, 2010. (DOI, PDF; Supporting Information: HTTP, PDF) - P. Lee, B.E. Griffith, and C.S. Peskin. The
immersed boundary method for advection-electrodiffusion with
implicit timestepping and local mesh refinement.
*J Comput Phys*, 229(13):5208-5227, 2010. (DOI, PDF) - B.E. Griffith, R.D. Hornung, D.M. McQueen, and
C.S. Peskin. Parallel and Adaptive Simulation of Cardiac
Fluid Dynamics. In M. Parashar and X. Li, editors,
*Advanced Computational Infrastructures for Parallel and Distributed Adaptive Applications*. John Wiley and Sons, Hoboken, NJ, USA, 2009. (DOI, PDF) - B.E. Griffith. An accurate and efficient
method for the incompressible Navier-Stokes equations using
the projection method as a preconditioner.
*J Comput Phys*, 228(20):7565-7595, 2009. (DOI, PDF) - P.E. Hand, B.E. Griffith, and C.S. Peskin.
Deriving macroscopic myocardial conductivities by
homogenization of microscopic models.
*Bull Math Biol*, 71(7):1707-1726, 2009. (DOI, PDF) - B.E. Griffith, X.Y. Luo, D.M. McQueen, and
C.S. Peskin. Simulating the fluid dynamics of natural and
prosthetic heart valves using the immersed boundary method.
*Int J Appl Mech*, 1(1):137-177, 2009. (DOI, PDF) - B.E. Griffith, R.D. Hornung, D.M. McQueen, and
C.S. Peskin. An adaptive, formally second order accurate
version of the immersed boundary method.
*J Comput Phys*, 223(1):10-49, 2007. (DOI, PDF) - B.E. Griffith and C.S. Peskin. On the order of
accuracy of the immersed boundary method: Higher order
convergence rates for sufficiently smooth problems.
*J Comput Phys*, 208(1):75-105, 2005. (DOI, PDF) - S.J. Cox and B.E. Griffith. Recovering
quasi-active properties of dendritic neurons from dual
potential recordings.
*J Comput Neurosci*, 11(2):95-110, 2001. (DOI, PDF) - L.J. Gray and B.E. Griffith. A faster Galerkin
boundary integral algorithm.
*Comm Numer Meth Eng*, 14(12):1109-1117, 1998. (DOI, PDF)

Submitted for publication (in alphabetical order by author)

- D. Devendran and B.E. Griffith. Comparison of two approaches to using finite element methods for structural mechanics with the immersed boundary method. Submitted.
- V. Flamini, A. DeAnda, and B.E. Griffith. Fluid-structure interaction model of the aortic root. Submitted.
- B.E. Griffith and X.Y. Luo. Hybrid finite difference/finite element version of the immersed boundary method. Submitted. (PDF)
- R.D. Guy, B. Phillip, and B.E. Griffith. Geometric multigrid for an implicit-time immersed boundary method. Submitted.

Theses

Revised 2014.07.04 by griffith@cims.nyu.edu.